$A$ $B$ $C$ If: $ BC = 8x + 8$, $ AC = 37$, and $ AB = 3x + 7$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 7} + {8x + 8} = {37}$ Combine like terms: $ 11x + 15 = {37}$ Subtract $15$ from both sides: $ 11x = 22$ Divide both sides by $11$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $BC$ $ BC = 8({2}) + 8$ Simplify: $ {BC = 16 + 8}$ Simplify to find ${BC}$ : $ {BC = 24}$